Each data set is derived from a library of formalized mathematics written in proof assistants Agda or Lean.

The declarative specification is closer to the problem description than the reasoning steps are, so the LLM can parse it out of the description more accurately. Furthermore, by offloading the actual reasoning task to an automated theorem prover, our approach can guarantee the correctness of the answer with respect to the parsed specification and avoid planning errors in the solving process.

Autoformalization addresses the scarcity of data for Automated Theorem Proving (A TP) by translating mathematical problems from natural language into formal statements. However, existing formalizer still struggles to consistently generate valid statements that meet syntactic validity and semantic consistency. To address this issue, we propose the Autoformalizer with Tool Feedback (A TF), a novel approach that incorporates syntactic and consistency information as tools into the formalization process. By integrating Lean 4 compilers for syntax corrections and employing a multi-LLMs-as-judge approach for consistency validation, the model is able to adaptively refine generated statements according to the tool feedback, enhancing both syntactic validity and semantic consistency. The training of A TF involves a cold-start phase on synthetic tool-calling data, an expert iteration phase to improve formalization capabilities, and Direct Preference Optimization to alleviate ineffective revisions. Experimental results show that A TF markedly outperforms a range of baseline formalizer models, with its superior performance further validated by human evaluations. Subsequent analysis reveals that A TF demonstrates excellent inference scaling properties. Recent advancements in the reasoning capabilities of large language models have significantly accelerated progress in the field of Automated Theorem Proving (A TP) (Y ang et al., 2024). Unlike traditional mathematical tasks, A TP requires models to start from a formalized theorem statement and construct rigorous logical proofs that can be verified within formal languages such as Lean (De Moura et al., 2015) and Isabelle (Paulson, 1994). However, the training of recent massive provers, such as DeepSeek-Prover (Ren et al., 2025) and Kimina-Prover (Wang et al., 2025), is hindered by the scarcity of formalized mathematical queries. Autoformalization addresses this by translating mathematical problems expressed in natural language into verifiable formal statements. A significant challenge in autoformalization is the absence of a universal automatic evaluation standard (Li et al., 2024b).

Formal verification is the next frontier for ensuring the correctness of code generated by Large Language Models (LLMs). While methods that co-generate code and formal specifications in formal languages, like Dafny, can, in principle, prove alignment with user intent, progress is bottlenecked by specification quality evaluation. Current benchmarks rely on matching against ground-truth specifications, a manual and expertise-intensive process that has limited existing datasets to a few hundred simple problems and also suffers from a reliability issue. To address this, we introduce VeriEquivBench, a new benchmark with $2,389$ complex algorithmic problems that probe the limitations of current models in both code generation and formal reasoning. Our evaluation framework replaces ground-truth matching with a formally grounded metric, the equivalence score, and rigorously verifies the quality of generated specifications and code. Our results show that generating formally verifiable code remains a profound challenge for state-of-the-art LLMs. This underscores both the difficulty of the task and the need for benchmarks like VeriEquivBench to drive progress toward scalable and reliable coding agents.

Recently, Language Models (LMs) have demonstrated complex reasoning capacities even without any finetuning.

Neuro-symbolic systems combine neural perception and logical reasoning, representing one of the priorities of AI research.